X(x-11)=840

Solution for X(x-11)=840 equation:

X(X-11)=840

We move all terms to the left:

X(X-11)-(840)=0

We multiply parentheses

X^2-11X-840=0

a = 1; b = -11; c = -840;
Δ = b2-4ac
Δ = -112-4·1·(-840)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-59}{2*1}=\frac{-48}{2}
=-24
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+59}{2*1}=\frac{70}{2}
=35
$